[Ifeffit] amplitude parameter S02 larger than 1

Scott Calvin scalvin at sarahlawrence.edu
Fri Mar 20 12:46:39 CDT 2015

```Hi Yanyun,

Lots of comments coming in now, so I’m editing this as I write it!

One possibility for why you're getting a high best-fit S02 is that the fit doesn't care all that much about what the value of S02; i.e. there is broad range of S02's compatible with describing the fit as "good." That should be reflected in the uncertainty that Artemis reports. If S02 is 1.50 +/- 0.48, for example, that means the fit isn't all that "sure" what S02 should be. That would mean we could just shrug our shoulders and move on, except that it correlates with a parameter you are interested in (in this case, site occupancy). So in such a case, I think you can cautiously fall back on what might be called a "Bayesian prior"; i.e., the belief that the S02 should be "around" 0.9, and set the S02 to 0.9. (Or perhaps restrain S02 to 0.9; then you're really doing something a bit more like the notion of a Bayesian prior.)

On the other hand, if the S02 is, say, 1.50 +/- 0.07, then the fit really doesn’t like the idea of an S02 in the typical range. An S02 that high, with that small an uncertainty, suggests to me that something is wrong—although it could be as simple as a normalization issue during data reduction. In that case, I’d be more skeptical of just setting S02 to 0.90 and going with that result; the fit is trying to tell you something, and it’s important to track down what that something is.

Of course, once in a while, a fit will find a local minimum, while there’s another good local minimum around a more realistic value. That would be reflected by a fit that gave similarly good quantitative measures of fit quality (e.g. R-factors) when S02 is fit (and yields 1.50 +/- 0.07) as when its forced to 0.90. That’s somewhat unusual, however, particularly with a global parameter like S02.

A good way to defend setting S02 to 0.90 is to use the Hamilton test to see if floating S02 yields a statistically significant improvement over forcing it to 0.90. If not, using your prior best estimate for S02 is reasonable.

If you did that, though, I’d think that it would be good to mention what happened in any eventual publication of presentation; it might provide an important clue to someone who follows up with this or a similar system. It would also be good to increase your reported uncertainty for site occupancy (and indicate in the text what you’ve done). I now see that your site occupancies are 0.53 +/- 0.04 for the floated S02, and 0.72 +/-0.06 for the S02 = 0.90. That’s not so bad, really. It means that you’re pretty confident that the site occupancy is 0.64 +/- 0.15, which isn’t an absurdly large uncertainty as these things go.

To be concrete, if all the Hamilton test does not show statistically significant improvement by floating S02, then I might write something like this in any eventual paper: “The site occupancy was highly correlated with S02 in our fits, making it difficult to determine the site occupancy with high precision. If S02 is constrained to 0.90, a plausible value for element [X] [ref], then the site occupancy is 0.53 +/- 0.04. If constrained to 1.0, the site occupancy is [whatever it comes out to be] To reflect the increased uncertainty associated with the unknown value for S02, we are adopting a value of 0.53 +/- [enough uncertainty to cover the results found for S02 = 1.0].

Of course, if you do that, I’d also suggest tracking down as many other possibilities for why your fit is showing high values of S02 as you can; e.g., double-check your normalization during data reduction.

If, on the other hand, the Hamilton test does show the floated S02 is yielding a statistically significant improvement, I think you have a bigger issue. Looking at, e.g., whether you may have constrained coordination numbers incorrectly becomes more critical.

—Scott Calvin
Sarah Lawrence College

On Mar 20, 2015, at 12:48 PM, huyanyun at physics.utoronto.ca<mailto:huyanyun at physics.utoronto.ca> wrote:

Hi Scott,

Thank you. Our group has one copy of your book, I'll read it again
after my colleague return it to shelf. I still want to continue our
discussion here:

If we treat S02 as an empirically observed parameter, can I just set
S02=0.9 or 1.45 and let other parameters to explain the k- and R-
dependence? Because S02 is not a simplistic parameter which may
include both theory and experimental effects, I feel that S02 is not
necessarily to be smaller than 1, although I admit S02 smaller than 1
is more defensible as it represents some limitations both in theory
model and experiment, but I have a series of similar sample and all
their S02 will be automatically be fitted to 1.45~1.55, not smaller
than 1. Could this indicate something?

I actually found in my system, when I set S02=0.9 (instead of letting
it fit to 1.45), other parameter will definitely change but the
fitting is not terrible, it is still a close fit but important site
occupancy percentage P% changed a lot.  So how should I compare/select
from the two fits, one with S02=0.9 and one with S02=1.45 with two
scenarios showing different results?

Best,
Yanyun
Quoting Scott Calvin <scalvin at sarahlawrence.edu<mailto:scalvin at sarahlawrence.edu>>:

Hi Yanyun,

I am hesitant to promote a commercial project from which I directly
profit on this list, but it seems to me you are asking a bigger set
of questions than can comfortably and sufficiently be answered in
this format, and they are questions which have been answered in
detail elsewhere.

In my book XAFS for Everyone, I have four pages devoted solely to
S02, along with related information elsewhere in the book.

Since you have a University of Toronto address, I am guessing you
have access to their library. If you don't wish to purchase the
book, you can request it via interlibrary loan, at no cost to you or

In the mean time, a quote from the book that may be useful in

"Alternatively, one can treat So2 as a phenomenological parameter
that accounts for any amplitude suppression independent of k and R,
regardless of physical cause (Krappe and
Rossner 2004). Under this view, So2 does not have any particular
physical meaning, and the k or R dependence of intrinsic losses can
be assigned to other parameters."

That's the way I usually think about it--as not having a single
physical meaning, but rather as being an empirically observed
correction factor relative to simplistic theories which is
indicative both of experimental effects and limitations in the
theoretical model.

Hope that helps...

--Scott Calvin
Sarah Lawrence College

On Mar 19, 2015, at 6:32 PM, huyanyun at physics.utoronto.ca<mailto:huyanyun at physics.utoronto.ca> wrote:

Hi all,

I know this question has been asked for many times. S02 is expected to
be around, but smaller than 1,  a fact that has been explained, such
as in the following previous emails, in our mailing list.

http://www.mail-archive.com/ifeffit%40millenia.cars.aps.anl.gov/msg02237.html
http://millenia.cars.aps.anl.gov/pipermail/ifeffit/2003-February/000230.html

However, I am continually get S02 value larger than 1 for a series of
similar samples when I fit data in Artemis. I think my fit is very
good, because my suspected model(based on other technique) could be
verified in XAFS analysis (i.e., defensible in physics), the
statistics is good ( R=0.01, reduced chi-square=31.4, fit-range:1.5~6
Angstrom, k-range: 3~14 angstrom-1) and all the parameters such as the
bond length, sigma2 are physically reasonable. The only thing makes me
uncomfortable is that parameter S02 keeps between 1.45 to 1.55 during
the fitting.

In my system, the absorber atom occupies two crystallographic sites.
So I built a model with paths generated from two FEFF calculations.
For paths generated from the 1st and 2nd FEFF calculation, the
amplitude parameters are set to be S02*P% and S02*(1-P%) respectively,
where P% is the first site occupancy percentage. Both S02 and P are
free parameters during the fit, and P is an important conclusion I
want to extract from XAFS fitting.

However, the fit result gives me S02=1.45 ~ 1.55 and P=0.51 ~ 0.56 all
the time (i.e., for each path the 'total amplitude' S02*P% or
S02*(1-P%) are about 0.7~0.8, smaller than 1). It looks to me that I
got a 'perfect' fit but I am not sure if S02 larger than one is
defensible. So I have to ask:

1) Is my current fit with S02 larger than one reasonable? If not, what
could be suggested to get around it?

2) What's the meaning of S02? It is interpreted in physics that it is
a reduced electron excitation parameter, but is it possible that S02
will be affected by any experimental condition?

3) Can anyone share whether you had the multiple site system that gets
S02 larger than one?

Best,
Yanyun

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